It's the same reason in english you are "on the computer". In danish you need to practise as well when to use om/i/på.
på mandag = on monday
om ugen = about the week / during the week
i maj = in may
As a Dane I find this sentence a little strange. It can make sense as an answer from a pregnant woman to the question "When is your due date?".
To say that your birthday is in May, you say "Min fødselsdag er i maj".
What would be the word for an appointment with the doctor? And what would it be for a date with a girl/boy (a romantic dinner for example)?
Yes, I see "dato" being used for a bigger appointment with a doctor. Something like an operation that has been scheduled some months in advance.
The word "dato" only refers to a calendar date in Danish, and does not have the more general meeting of a (romantic) meeting. There we would actually often use the English word: "Jeg skal på en date i aften!" means "I'm going on a date tonight!".
Jeg ville sige: min fødselsdato er i maj, ellers bruger man kun dato i forretnings breve .f.ex H"
can anyone explain what does this sentence mean? what is the definition of one's "date"?
It is a certain day that somehow pertains you. Kind of an appointment. But it sounds pretty strange in Danish. Usually you don't personalise dato, but just say "Datoen er i maj" - "The date (of the occurrence) is in May."